Features and Results

Key Features of ndCurveMaster:

• Fully automated process to curve fit your dataset.
• Automated discovery of nonlinear equations.
• Auto data fitting for an unlimited number of variables and their combinations.
• Polynomial fitting of any order for any number of variables, including a set of templates for polynomial functions.
• Heuristic techniques for data fitting using random iterated or full random search algorithms.
• Comprehensive statistical analysis for each equation, including analysis of variance (ANOVA), regression, and collinearity.
• Multicollinearity detection through the use of Variance Inflation Factor (VIF) and Pearson Correlation Matrix.
• Search for models with a VIF limit value.
• Ability to weight data for individual data points in any column.
• Detect and prevent overfitting.
• Models with or without an intercept term.
• User-controlled model expansion or reduction.
• Import data from CSV, TXT, XLSX, XLS spreadsheets.
• Result history and ranking features.
• Access to up to 380 basic functions such as power, exponential, logarithmic, and trigonometric functions grouped in 5 collections, plus a user-created custom function collection.
• Options to copy, save, or load results.
• High-quality plots including 2D fitted lines, regression, residual plots, and histograms.
• Set any significant level for alpha value.
• Optimized to manage large amounts of data.
• Normality assessment of regression residuals with a Q-Q plot without modifying a preselected predictor variable during the search.

ndCurveMaster allows you to automatically fit a variety of models to your data, for example:

This program provides the development of a regression model for any number of input variables without any limitations. These models can be created using fully automatic search or manually by the user. The following types of models can be automatically discovered:

• Multiple Nonlinear Regression (MNLR) model, for example: Y = a0 + a1 · exp(x1)-0.5 + a2 · (ln(x2))8 + a3 · exp(x3)1.5 + a4 · x44.1 + a5 · x55 + a6 · x66
• MLNR model with variable combination, for example: Y = a0 + a1 · exp(x1)-0.1 + a2 · x2 + a3 · x3 + a4 · x4(1/8) + a5 · x10.9 · x20.9 + a6 · x11.35 · x3 + a7 · (ln(x1))5 · ln(x4) + a8 · x2 · x3 + a9 · (ln(x3))8 · x40.55 + a10 · x11.25 · x2 · x3 + a11 · x2(1/2) · x36 · x40.8
• Any order Polynomial Regression Model, for example: Y = a0 + a1 · x1 + a2 · x2 + a3 · x3 + a4 · x1 · x2 + a5 · x1 · x3 + a6 · x2 · x3 + a7 · x1 · x2 · x3 + a8 · x12 + a9 · x22 + a10 · x32 + a11 · x13 + a12 · x23 + a13 · x33 + a14 · x12 · x2 + a15 · x1 · x22 + a16 · x12 · x3 + a17 · x1 · x32 + a18 · x2 · x32 + a19 · x22 · x3 + a20 · x12 · x2 · x3 + a21 · x1 · x22 · x3 + a22 · x1 · x2 · x32
• Regression model consisting of only input variable combination, for example: Y = a1 · x10.1 · x20.2 · x3(-1/12) · x4(-1/12) · x55

ndCurveMaster offers the ability to manually develop a regression model, utilizing the user's knowledge and experience. The following models can be developed through this method:

• Non-linear model of any form, for example: Y = a0 + a1 · (ln(x1))8 + a2 · (ln(x2))7 + a3 · exp(x3)1.5 + a4 · x4-11 + a5 · x55
• Logarithmic transformed models, such as:
  Linear-log model, for example: Y = a0 + a1 · ln(x1) + a2 · ln(x2) + a3 · ln(x3) + a4 · ln(x4) + a5 · ln(x5)
  Log-linear model, for example: ln(Y) = a0 + a1 · x1 + a2 · x2 + a3 · x3 + a4 · x4 + a5 · x5
  Log-log model, for example: ln(Y) = a0 + a1 · ln(x1) + a2 · ln(x2) + a3 · ln(x3) + a4 · ln(x4) + a5 · ln(x5)
• Multiple linear regression model (MLR), for example: Y = a0 + a1 · x1 + a2 · x2 + a3 · x3 + a4 · x1 · x2 + a5 · x1 · x3 + a6 · x2 · x3 + a7 · x1 · x2 · x3

In addition, every model may:

• contain the intercept value: Y = a0 + a1 · x1 + ...
• not contain the intercept value: Y = a1 · x1 + ...

Each developed model can be freely expanded or reduced, either automatically or manually by the user. This way, the user can precisely fit any model to the data.

ndCurveMaster features advanced tools for verifying and enhancing the accuracy of developed models, such as:

Analysis of variance (ANOVA):

Regression analysis

Multicollinearity prevent and detection by using Variance Inflation Factor (VIF):

Multicollinearity detection by using Pearson Correlation matrix:

Detailed information about multicollinearity can be found here.

Overfitting detection

Detailed information about overfitting can be found here.

ndCurveMaster quickly generates high quality graphs as follows:

2D Fitted Line Plot

Scatterplot

Residuals

Standardized Residuals

Histogram